Abstract
Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the "bald-spots" created by topological point defects, thus paving the way for atomic chemistry at micron scales. We show that singular wall defects, topologically unstable "bald lines" in two dimensions, are stabilized near the order-disorder transition on a sphere. We attribute their stability to free-energetic considerations, which override those of topological stability.
Highlights
The remarkable interplay between the curvature of a surface and frustration of orientational order on it is strikingly demonstrated by the Poincaré-Hopf index theorem [1]
In this paper we have used a simplified version of the Ginzburg-Landau theory to predict the existence of stable topological wall defects on spheres with n-atic order
In our analysis we have ignored the effects of thermal fluctuations
Summary
The remarkable interplay between the curvature of a surface and frustration of orientational order on it is strikingly demonstrated by the Poincaré-Hopf index theorem [1]. Rigid spheres have been prepared by molecular coating of ordered tilted monolayer on metal nanospheres [5], leading to the antipodal configuration of a source-sink pair of disclinations of index 1 each We show that singular wall defects can be stabilized on a sphere because of its Gaussian (intrinsic) curvature, and not because of boundary conditions, externally imposed fields, or divergences in certain elastic constants. They are stable close to the order-disorder transition, over a finite range of a dimensionless parameter η. To the best of our knowledge, such defects have not been discussed in condensed matter systems
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